WASHINGTON—The first glimpse many Americans got of Marion Barry, the longtime Washington, D.C., politician, was of Federal Bureau of Investigation surveillance footage showing the then-mayor smoking crack in a hotel room with a woman not his wife.

Mr. Barry, who died early Sunday at the age of 78, was then in his third term as mayor of the nation’s capital. He retained his popularity for decades after the 1990 crack incident. After serving time in federal prison on a drug charge, he returned to be elected mayor in 1994 for...